Rectangular trapezoid is divided by the diagonal into right-angled and equilateral triangles

Rectangular trapezoid is divided by the diagonal into right-angled and equilateral triangles, find the midline of the trapezoid if the perimeter of an equilateral triangle is 27.

Find the side of an equilateral triangle by dividing its perimeter by 3.

27: 3 = 9 units.

The middle line of a trapezoid is equal in our case to the sum of the middle lines of each of the two triangles formed by its diagonal.

Find the midline of an equilateral triangle:

L1 = 9: 2 = 4.5 units.

Find the midline of a right-angled triangle:

L2 = 4.5: 2 = 2.25 units.

Find the middle line of the trapezoid:

4.5 + 2.25 = 6.75 units.

Answer: The middle line of the trapezoid is 6.75 units.